Place 16 mini silicone muffin cases on a baking sheet.
Put the butter and sugar in a bowl and beat until pale and fluffy. Beat in the egg yolk and white, then add the flour and mix to make a firm dough. Knead into a ball, wrap in clingfilm and chill for at least 30 minutes.
Divide the dough in half and press half the dough into the cases. Push a piece of fudge down into the centre of each case. Divide the remaining dough into 16 pieces. Roll each piece into a ball using lightly floured hands and flatten into a round roughly 5 cm (2 inches) in diameter. Push a circle of dough into each case, covering the fudge, and press it down firmly around the edges.
Bake in a preheated oven, 190°C (375°F), Gas Mark 5, for 15–20 minutes, or until slightly risen. Leave in the cases for 5 minutes, then transfer to a wire rack to cool. Serve lightly dusted with icing sugar.